Step-by-step explanation:

[tex]volume \: of \: \: cylindrical \: tank \: = \pi {r}^{2} h \\ = 3.14 \times {60}^{2} \times 95 \: {cm}^{3} \\ = 1073880 \: {cm}^{3} [/tex]

[tex]volume \: of \: rectangular \: sump = length \times breadth \times height \\ = 157 \times 144 \times 95 \: {cm}^{3} \\ = 2147760 \: {cm }^{3} [/tex]

Volume of sump after filling overhead tank = volume of sump before filling - volume of tank

[tex] = (2147760 - 1073880) {cm}^{3} \\ = 1073880 \: {cm}^{3} [/tex]

Let the height of water in sump after filling be h

A.T.Q.

157 × 144 cm^2 ×h = 1073880 cm^3

h = (1073880 cm^3)/(157×144 cm^2)

h = 47.5 cm

capacity of tank / capacity of sump = volume of tank / volume of sump

= (1073880 cm^3) / (2147760 cm^3)

= 1/2

Verified answer

✯Question:-

Selvi’s house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (an underground tank) which is in the shape of a cuboid. The sump has dimensions 1.57 m × 1.44 m × 95cm. The overhead tank has a radius of 60 cm and a height of 95 cm. Find the height of the water left in the sump after the overhead tank has been completely filled with water from the sump which had been full. Compare the capacity of the tank with that of the sump. (Use π = 3.14)

✯Answer:-

Height of the water in the sump = 47.5 cm

✯Explanation:-

Volume of water in the overhead tank = Volume of the water removed from the sump.

Volume of water in the overhead tank = [tex]3.14 \times 0.6 \times 0.6 \times 0.95[/tex]

[tex] = > 3.14 \times 0.36 \times 0.95[/tex]

Volume of water in the sump when it is full of water = [tex]1.57 \times 1.44 \times 0.95[/tex]

[tex] = 1.57 \times 4 \times 0.36 \times 0.95[/tex]

[tex] = > 2 \times 3.14 \times 0.36 \times 0.95[/tex]

Volume of water left in the sump after filling the tank

[tex](2 \times 3.14 \times 0.36 \times 0.95 - 3.15 \times 0.36 \times 0.95) {m}^{2} = 3.14 \times 0.36 \times 0.95 \: {m}^{2} \\ [/tex]

Area of the bottom of the sump = [tex]1.57 \times 1.44 \: {m}^{3} [/tex]

[tex] = 1.57 \times \times 4 \times 0.36 \: {m}^{3} [/tex]

[tex] = > 2 \times 3.14 \times 0.36 \: {m}^{3} [/tex]

Height of the water in the sump =

[tex] \frac{3.14 \times 0.36 \times 0.95}{2 \times 3.14 \times 0.36} m \\ [/tex]

[tex] = \frac{0.95}{2} \\ [/tex]

[tex] = 47.5 \: cm[/tex]

[tex] \frac{Capacity \: \: of \: \: Tank }{Capacity \: \: of \: \: Sump } = \frac{3.14 \times 0.36 \times 0.95}{2 \times 3.14 \times 0.36 \times 0.95} \\ [/tex]

[tex] = \frac{1}{2} \\ [/tex]